Some Improvements on Hilbert's Integral Inequality

A method for producing spun yarn in an open-end spinning system having a rotary open-ended spinning chamber comprises feeding a bundle of fibers to the open-ended spinning chamber, rotating the open-ended spinning chamber at a peripheral surface speed V to successively accumulate superimposed layers of fibers upon the peripheral surface of the spinning chamber, withdrawing the accumulated fiber layers from the rotating open-ended spinning chamber in the form of spun yarn at a withdrawing speed W to self-double the spun yarn at a doubling number V/W, and selectively varying the speeds V and W to provide the spun yarn with a predetermined doubling number V/W during only a single passage through the open-end spinning system. The bundle of fibers is fed to the spinning chamber in a compressed air stream which transports the fibers in a mutually liberated condition to the open-ended spinning chamber.